A beam: need to calculate its max moment and deflection

[Poke]

Homework Statement

Beam spans 40 feet, with uniform loading of 500 pound/feet and a point load of 4000 pound at mid span.
Support A is roller, support B is pin.
How to determine the maximum moment and maximum deflection due to the loads.
Use Force method

Since it is a Determinate structure, I am not very sure how to use the method.

Homework Equations

Delta + f F = 0

find Delta

The Attempt at a Solution

I suppose I need to add a virtual force of 1 pulling the structure down at mid span... so that it generates 2 virtual moments (m).

From the original structure, I can also get 2 real moments (M).

Then using the equations:

Delta = integration of m*M / EI ...
f = integration of m*m / EI

And then I will know deformation??

 

[PhanthomJay]

I guess that's the unit load method for determining deflections. When calculating M and m you need to show it as a function of x.
And since fthe applied and virtual point loads result in a discontinuity In moment, you have to write 2 equations for the moments, one for the left side of center, and one for the right. Then do the integrations and add them all up